In various systems, this usually means you get a set of points (typically once per session) you can use to add to a die roll once in a while, when it's really important.

In my system I use these to allow players to add to critical die rolls (or whenever they want to) as yet another 'Free Dice'.

I base them on three possible personality archetypes, Piety, Honor, or Elan.

Each type requires you to adhere to certain behaviors in order to maintain the action points. You get them at a rate of 1 point per level per session.

Piety means you are a deeply religious person (not precisely the same thing as 'spiritual') and you follow the orthodoxy of the religion, more or less as a typical Medieval person would do. So in my campaigns which are usually set in 15th Century Europe, that means that you have to attend mass regularly, fast during lent and on Fridays and other fast days, obey Christian law, and when you Sin you have to make confession before an ordained priest. When you are in a state of Sin either you don't get your action points (they aren't available) or you may just loose one or two for each 'sin' (such as killing someone). If you do something really sinful, like kill a priest or commit adultery or something, you may have to go on a pilgrimage to recover your Piety points.

Honor means you hold to a high standard of personal 'honor' as in Feudal Japan, or as among the Celts or Romans or most of the warrior class in Medieval Europe (and a lot of the rest of the world). If anyone sleights you in any way, you lose honor points. This can include ridiculous things like suffering a petty insult, or someone else being seated closer to the guest of honor at a feast than you are, or someone failing to greet you in the proper way. Whenever this happens, you lose an 'honor point' until and unless you regain it (such as by cuffing this person with the back of your hand and calling them a knave!). A lot of this also depends on if anyone sees you being dishonored, as in my context honor is directly related to reputation (fama, in the Medieval jargon). If you suffer a grave dishonor, such as you break an oath, are cuckolded or defeated by a lesser opponent, or show cowardice, you will have to go on a quest, or fulfill a great vow, such as vowing in public to kill a very dangerous opponent and then actually doing so.

Elan means you live by passion, for the thrill in life, and keep up a sense of style. You suffer from the mundane and the depressing. If you are eating well, drinking, sleeping with women, you are up to your maximum capacity of Elan points. If you are sleeping in the stable, walking for days in the rain, forced to do tedious work, you lose your points. Both honor based and elan based characters may suffer (lose their points) under these conditions, whereas a piety based character will not, so long as they remain in communion.

In all three cases, it's possible to also get extra temporary points by doing something particularly pious, or honorable, or stylish. So for example recovering an important religious relic from the heathens (and returning it to the Church), showing chivalry on the battlefield (such as releasing an enemy who might come back to get you), or stealing a great treasure from a dangerous rival (even more point if you then, gave it away or burned it), respectively, could gain you an extra action point.

This is what I have so far. What I have not done yet is defined precisely how piety works for a non Christian character (have to do more research) and I'm not sure if or how exactly I should limit how these action points are spent (might be a good idea to limit them to one per die roll) and how they 'recharge'. Initially I thought once per session but other times I let it be once per 'scene' or once per day, because players would do things mid game to recover their points (like seek out a priest for confession or make a vow and slay a dangerous enemy and so on.

If and when I can work out all the gray areas a bit better I'll probably add this as an optional rule to the system.

I have implemented a similar thing in my game, based on some rules that I got from somewhere I don't remember. I use it to encourage my players to support each other and not do stupid things that get other characters killed. Basically, each character has a morale rank. It goes up by one every other level. Characters that are new to the group start at rank 1 no matter their level and go up by 1 for every month they're with the group until they catch up to the others. Acts of cowardice or acts that endanger other members of the group lower your rank by 1. Each character gets their rank in free dice per session. They can choose to put any number of their free dice into a common pool at the start of the game. I've only used it in one session so far, but it has worked quite well. I think it would work especially well for a "band of brothers" type game where all the characters are soldiers.